Mark the ABS pipes entering each side of the coupling 6 inches from where the pipes enter the coupling. Cut all the way through both pipes at the marks using a handsaw. Make the cuts straight. Discard the broken coupling. Remove all burrs from the pipe cuts with a utility knife.
Apply ABS cement around the outside of both existing pipe ends. Then cement one inside end of two straight (180-degree) ABS couplings. Quickly push the cemented ends of the couplings onto the pipe ends, holding them in position for five seconds while the cement dries.
Push 8 inch (or longer) sections of ABS pipe into each end of a new ABS coupling (with the same angle as the old broken coupling), using no cement at this time. Hold the new coupling and pipe sections in position against the existing cut pipe ends, and mark on each pipe the place where they will enter the new installed couplings (allow for how far they will enter each coupling's inlet).
Take the new pipe sections out of the new coupling, and cut both pipes at the marks. Remove any burrs. Apply ABS cement to one outside end of both new pipes, and the inside ends of the new coupling. Push the pipe ends into the coupling and hold in place for five seconds.
Cement the other ends of the new pipes, and the remaining inside ends off the installed straight couplings. Push the pipe ends into the straight couplings, and hold in place for five seconds.